Properties

Label 6025.62
Modulus $6025$
Conductor $6025$
Order $240$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6025)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([108,101]))
 
pari: [g,chi] = znchar(Mod(62,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.iz

\(\chi_{6025}(62,\cdot)\) \(\chi_{6025}(92,\cdot)\) \(\chi_{6025}(112,\cdot)\) \(\chi_{6025}(202,\cdot)\) \(\chi_{6025}(327,\cdot)\) \(\chi_{6025}(372,\cdot)\) \(\chi_{6025}(513,\cdot)\) \(\chi_{6025}(538,\cdot)\) \(\chi_{6025}(552,\cdot)\) \(\chi_{6025}(628,\cdot)\) \(\chi_{6025}(672,\cdot)\) \(\chi_{6025}(778,\cdot)\) \(\chi_{6025}(922,\cdot)\) \(\chi_{6025}(1212,\cdot)\) \(\chi_{6025}(1247,\cdot)\) \(\chi_{6025}(1342,\cdot)\) \(\chi_{6025}(1412,\cdot)\) \(\chi_{6025}(1433,\cdot)\) \(\chi_{6025}(1497,\cdot)\) \(\chi_{6025}(1603,\cdot)\) \(\chi_{6025}(1733,\cdot)\) \(\chi_{6025}(1797,\cdot)\) \(\chi_{6025}(1962,\cdot)\) \(\chi_{6025}(2027,\cdot)\) \(\chi_{6025}(2042,\cdot)\) \(\chi_{6025}(2098,\cdot)\) \(\chi_{6025}(2113,\cdot)\) \(\chi_{6025}(2138,\cdot)\) \(\chi_{6025}(2162,\cdot)\) \(\chi_{6025}(2253,\cdot)\) ...

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

\((2652,2176)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{101}{240}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\(1\)\(1\)\(e\left(\frac{49}{120}\right)\)\(e\left(\frac{89}{120}\right)\)\(e\left(\frac{49}{60}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{161}{240}\right)\)\(e\left(\frac{9}{40}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{173}{240}\right)\)\(e\left(\frac{67}{120}\right)\)\(e\left(\frac{79}{240}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{240})$
Fixed field: Number field defined by a degree 240 polynomial